Extract

It is known that Maclaurin’s spheroid of rotating liquid becomes unstable when its eccentricity reaches the value sin 54° 21' 27''. This is a form of bifurcation, and for increasing momentum the stability passes over to Jacobi’s ellipsoid. It is possible to prove these results by the method applied by me to the discussion of the stability of the pear-shaped figure of equilibrium, and it is worth while to do so, because we obtain thereby a verification of the complicated analysis used in the previous investigation, and because the series which arise are exactly similar to the former series. In vol. 3 of my ‘Scientific Papers’ I shall give a few details about the present analysis. It will here suffice to say that it gives the known results correctly, and a good approximation to the form of Jacobi’s ellipsoid.

Footnotes

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